NucleonNucleon interaction qualitative analysis Characteristic radius r fm

Nucleon-Nucleon interaction (qualitative analysis) Characteristic radius r (fm) b=1. 4 fm QCD! V(r) OPEP+pg p breaks isospin + TPEP+… (energy dependent…) quark-gluon structures overlap poorly known; experimental data are not sensitive to large momentum transfer w heavy mesons

Nucleon-Nucleon interaction Scattering Analysis pp, nn scattering in T=0, 1 channels • pp scattering easy • neutron beams (np, nn) and neutron targets (pn, nn) difficult 7 Li(p, n), reactors short neutron lifetime (~10 min) deuteron - a substitute (pp and 3 N effects have to be subtracted); Scattering Cross Section k k’ z elastic scattering; the same value of k! valid for short-ranged potentials (V=0 at large r) Coulomb contribution is removed

Nucleon-Nucleon interaction Partial-wave decomposition For scattering off a short-ranged potential, it is useful to carry out a partial-wave decomposition. phase shift The probability current density in each partial wave is conserved - unitarity (valid only for elastic scattering!). The partial wave decomposition is very convenient at low energies since only a few terms enter the expansion. potential range For pn scattering (potential range 2 fm) and low momenta (<400 Me. V/c), the swaves dominate. The phase shift d 0 is decisive for nuclear binding. 2 S+1 L J For momenta > 400 Me. V/c the phase shift is negative. This indicates that the nuclear force is repulsive at short distances!

Nucleon-Nucleon interaction Partial-wave decomposition hard core attractive square well

Nucleon-Nucleon interaction (phase shift analysis) V (Me. V) 1 S 0 1 D 2 The realistic NN potential is a function of the total spin S of the two nucleons. The conserved quantity is To determine S (=0 or 1) one needs polarization data! 1 S 0 3 S 1 Paris potential

Nucleon-Nucleon Interaction Realistic NN forces Selected Phase Shifts with V 18

Nucleon-Nucleon interaction (inelastic scattering) With sufficient energy, scattering can excite the internal degrees of freedom of the nucleons: can produce secondary particles: or baryon-antibaryon pairs: Since the mass of the pion is about 140 Me. V, pion production takes place above this threshold. Inelastic scattering represents a loss of flux in the incident channel, hence the probability amplitude is no longer conserved. Such a situation may be described by a complex scattering potential.

Nucleon-Nucleon interaction (Scattering length and effective range) At low energies, the total cross section remains finite for NN scattering length is positive if there is a bound state effective range

Nucleon-Nucleon interaction Deuteron Binding energy 2. 225 Me. V Spin, parity 1+ Isospin 0 Magnetic moment m=0. 857 m. N Electric quadrupole moment Q=0. 282 e fm 2 produced by tensor force! kinetic energy is comparable to the depth of the potential rms radius=1. 963 fm

Nucleon-Nucleon Interaction NN, NNNN, …, forces GFMC calculations tell us that: short-range three-body N-body forces scale as: naturalness!

Nucleon-Nucleon Interaction Realistic NN forces Deuteron Structure Functions with V 18

Nucleon-Nucleon Interaction Realistic NN forces Deuteron Shapes with V 18 http: //www. phy. anl. gov/theory/movie-run. html

Nucleon-Nucleon Interaction Realistic NN forces One-body Densities

Nucleon-Nucleon Interaction Realistic NN forces Two-body Densities

Few-nucleon systems (theoretical struggle) A=2: many years ago… 3 H: 1984 (1% accuracy) • Faddeev • Schroedinger 3 He: 1987 4 He: 1987 5 He: 1994 (n-a resonance) A=6, 7, . . 10: 1995 -2002

Few-nucleon systems (theoretical methods) Green’s Function Monte Carlo (imaginary-time method) Trial wave function (taken from VMC) Other methods: • • • Faddeev-Yakubovsky method Hyperspherical harmonics method Coupled-cluster expansion method, exp(S) Cluster approaches (resonating group method) No-core shell model Molecular dynamics